Eigensolution analysis of spectral/hp continuous Galerkin approximations to advection–diffusion problems: Insights into spectral vanishing viscosity
DOI: 10.1016/j.jcp.2015.12.009
Abstract: This study addresses linear dispersion–diffusion analysis for the spectral/hp continuous Galerkin (CG) formulation in one dimension.

Linear dispersion–diffusion analysis and its application to under-resolved turbulence simulations using discontinuous Galerkin spectral/hp methods
DOI: 10.1016/j.jcp.2015.06.020
Abstract: We investigate the potential of linear dispersion–diffusion analysis in providing direct guidelines for turbulence simulations through the under-resolved DNS (sometimes called implicit LES) approach via spectral/hp methods. The discontinuous Galerkin (DG) formulation is assessed in particular as a representative of these methods. We revisit the eigensolutions technique as applied to linear advection and suggest a new perspective to the role of multiple numerical modes, peculiar to spectral/hp methods.